AbstractThis paper derives a Fourier‐like expansion formula in the signal space composed of spline functions, with the sampled value sequence of the signal as the expansion coefficients. Here, the domain is a finite closed interval and the boundary condition is periodic. The signal space composed of spline functions is one of the generalizations of the band‐limited signal space with the continuous differentiability as the parameter. Consequently, the Fourier‐like expansion formula derived in this paper is a generalization of Cahn's sampling theorem in the band‐limited signa